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%I #11 Mar 16 2022 02:54:06
%S 1,4,182,27410,8890310,5051270688,4459786293372,5659222645997646,
%T 9770821427711370950,22041005972637205198568,
%U 62967534725721252354766676,222256499446324679350316816644,950020052553444052606973276792092,4836606673194788521307702032786510240,28920975283745982162014025622769293094712
%N a(n) = A142458(2*n-1, n)/n.
%H G. C. Greubel, <a href="/A172018/b172018.txt">Table of n, a(n) for n = 1..190</a>
%F a(n) = A142458(2*n-1, n)/n.
%t T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k-m+1)*T[n-1, k, m]];
%t A172018[n_]:= T[2*n-1, n, 3]/n;
%t Table[A172018[n], {n, 30}] (* modified by _G. C. Greubel_, Mar 16 2022 *)
%o (Sage)
%o @CachedFunction
%o def T(n,k,m):
%o if (k==1 or k==n): return 1
%o else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
%o def A172018(n): return T(2*n-1, n, 3)/n
%o [A172018(n) for n in (1..30)] # _G. C. Greubel_, Mar 16 2022
%Y Cf. A142458, A172010.
%K nonn
%O 1,2
%A _Roger L. Bagula_, Nov 19 2010
%E Offset changed and more terms added by _G. C. Greubel_, Mar 16 2022